A New Take on the "Coffee Savings Plan"

You all have seen the savings of cutting out that one cup of Starbucks per day, but I haven't seen anyone plug this savings into an annuity equation, so I give you here what could happen.

Here are the assumptions:
$5 per cup of coffee (Latte with flavor),

Purchases are made only Monday through Friday, at 1 cup per day.
5% APY (I'm assuming a high yield savings account).

An estimate of the future value (fv) of money can be easily calculated in two ways:

For a single deposit, earning interest at a constant rate, use this equation:

For an annuity, that is a fixed amount deposited at regular intervals (derived from annual, but can be used for smaller intervals), can be calculated with the equation:

So, what do those letters mean?  Well, P is your deposit or principal, R is the rate of return and N is the number of times it's compounded.

In this case, the total principal to be deposited is $5/day * 5 days/week * 52 weeks = $1300, an average of $108.33 per month.  The rate is about 0.42%... Wait I said the APY is 5%, so where'd this 0.42% come from... It's the approximate monthly rate or MPY.  And of course, since we're working with months and want to see the results from 1 year, the number of times compounded is 12.

So, with all this in hand, how much are we REALLY saving?

Let's say for the sake of argument that the full $1300 was available at the beginning of the year and we deposited it all at once, then we'd have about $1366.51 (give or take a few cents, since these equations are only estimates).

Realistically, those of us trying to get out of debt can't really afford to dump the full $1300 in at the beginning of the year, so we'd probably budget the $108.33 per month as an annuity for the year, netting $1330.21 by year end.

Converting either the annuity or single amount for partial or multiple years is as easy as changing N, but what about putting $1300 in once per year for X years?  Or just putting the $108.33 in for one year and then letting it sit?  Well, there is no simple equation, though you could plug the result of the annuity into the single time equation.  But converting the $1300 into an annual annuity with monthly compounding, not so easy.  To solve these and other problems, I WILL work on deriving equations that will make it possible, though it may take me some time and they won't necessarily be pretty.

So, the moral of this exercise, don't just cut the coffee, put the money into your high-yield savings account or for better potential returns, invest it.